How to Calculate the Tax Multiplier
The tax multiplier equals −MPC ÷ MPS; multiply it by the change in taxes to find the change in GDP. It is negative and smaller than the spending multiplier.
Formula
Steps
- 1Find the MPC and MPS. MPC is the fraction of extra income spent; MPS = 1 − MPC.
- 2Compute the multiplier. Tax multiplier = −MPC ÷ MPS. The negative sign means taxes and GDP move in opposite directions.
- 3Apply it to the tax change. ΔGDP = tax multiplier × Δtaxes. A tax cut is a negative Δtaxes, so it raises GDP.
Worked example
If MPC = 0.75, the tax multiplier = −0.75 ÷ 0.25 = −3. A $20B tax cut (Δtaxes = −$20B) changes GDP by −3 × (−20) = +$60B — versus +$80B if the government had spent $20B directly (multiplier 1 ÷ 0.25 = 4).
Frequently asked questions
Why is the tax multiplier weaker than the spending multiplier?
Government spending enters aggregate demand dollar-for-dollar in round one, but a tax cut first becomes disposable income and households save the MPS share — only the MPC share is spent initially.
What is the balanced budget multiplier?
If spending and taxes rise by the same amount, the effects net to a multiplier of 1: spending multiplier + tax multiplier = 1 ÷ MPS + (−MPC ÷ MPS) = 1. GDP rises by exactly the amount spent.
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